SPM 2017 Add Maths Paper 1, Question 16Circular Measure

Solved on video in English and Bahasa Melayu · 3 marks · Form 5, Circular Measure · 4:25 video

The question

Diagram 7 shows two sectors AOD and BOC of two concentric circles with centre O. The angle subtended at the centre O by the major arc AD is 7alpha radians and the perimeter of the whole diagram is 50 cm. Given OB = r cm, OA = 2OB and angle BOC = 2alpha, express r in terms of alpha.

[3 marks]

SPM 2017 Add Maths Paper 1, Question 16: the question as drawn in Eduly's video4:25

Step 1

Length of major arc AD (radius OA = 2r, angle 7alpha) = 2r * 7alpha = 14r*alpha.

Why this step

Each arc sits on its own circle, so use that circle's radius. The major arc AD is on the big circle, so use 2r, not r.

5 more steps, each with the reason for it, in the full solution

Final answer

r = 25/(8α + 1)

Where students lose marks

Watch out: use radius 2r for the major arc AD (not r), and include both straight sides AB and DC in the perimeter.

Watch every step of this question solved on video (4:25), with the reason behind each step and a box that checks your own answer.

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